Regional Optimal Control Problem Governed by Distributed Bi-linear Hyperbolic Systems

This paper considers the regional bi-linear control problem of an important class of hyperbolic systems. The objective is to bring the state solutions at time T close to a desired observations w ^d only on a sub-region ω along the spatial domain Ω. We prove the existence of solution by minimizing sequence method. The adjoint system of this problem is introduced and used to characterize the optimal control. A numerical approach is developed and illustrated successfully by simulations.